directed set


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directed set

[də′rek·təd ′set]
(mathematics)
A partially ordered set with the property that for every pair of elements a,b in the set, there is a third element which is larger than both a and b. Also known as directed system; Moore-Smith set.

directed set

(theory)
A set X is directed under some relation, <= (less than or equal), if it is non-empty and if for any two elements x and y there exists an element z such that x <= z and y <= z. I.e. all pairs have an upper bound.
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Father-of-two Celyn, who now lives in the north west of England, developed the idea for the film with Pembrokeshireborn Andy Goddard, who directed Set Fire To The Stars and has a long career in TV, including work on Downton Abbey.
Ghosh's erudition and dogged scholarship are extremely impressive; the sense he provides of Weber's craft in shaping, even distorting, the extensive and amorphous array of historical material into a coherent and clearly directed set of concepts is salutary.
that [theta]-converges to y and J be a directed set.
Since I is a directed set, i [less than or equal to] [i.
finding some directed set of questions and insights that converges on the discovery of the key mathematical relationship is essential.